We solve this optimization problem using an interval-value iteration as detailed in [1]}, which results in a memoryless strategy on \(\mathcal {P}\) . The interval-value iteration procedure also returns the lower- and upper-bounds of the probability of satisfaction of \(\varphi \)  under \(\pi _{\text{off}}\) , i.e.,
\(\underline{p}_{\pi _{\text{off}}}(s) &= \min _{\xi \in \Xi } P[_\mathcal {P}\models \varphi \mid \pi _{\text{off}}, _\mathcal {P}(0) = s], \\\overline{p}_{\pi _{\text{off}}}(s) &= \max _{\xi \in \Xi } P[_\mathcal {P}\models \varphi \mid \pi _{\text{off}}, _\mathcal {P}(0) = s],\) 
